Miscounts, Duverger's Law and Duverger's Hypothesis

Abstract

In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small.

All robust equilibria of plurality voting games satisfy Duverger's Law: In any robust equilibrium, exactly two candidates receive a positive number of votes. Moreover, robustness (only) rules out a victory of the Condorcet loser.

All robust equilibria under runoff rule satisfy Duverger's Hypothesis: First round votes are (almost always) dispersed over more than two alternatives. Robustness has strong implications for equilibrium outcomes under runoff rule: For large parts of the parameter space, the robust equilibrium outcome is unique.